On block designs arising from rank 3 graphs

In this paper a criterion showing when the orbit of a subgraph of a given rank 3 graph forms a block design, is given. As an application several classes of block designs are derived from the triangular graph T(n) and the lattice graph L₂(n).     

Unified treatment of Cramér-Rao bound for the nonregular density functions

This paper extends the idea of Vincze (1978) and unifies the approach for the uniparameter and multiparameter situations for obtaining the Cramér-Rao inequality.     

Second order asymptotic relations of M-estimators and R-estimators in two-sample location model

Let T_M be an M-estimator (maximum likelihood type estimator) and T_R be an R-estimator (Hodges-Lehmann's estimator) of the shift parameter Δ in the two-sample location model. The asymptotic representation of √N(T_M-T_R) up to a term of the order O_p(N^{-$\text{1}\text{4}$}) is derived which is valid if the functions Ψ and ? generating T_M and T_R, respectively, decompose into an absolutely continuous and a step-function components; the order O_p(N^{-$\text{1}\text{4}$}) cannot be improved unless the discontinuous components vanish. As a consequence, the conditions under which √N(T_M-T_R)=O_p(N^{-$\text{1}\text{4}$}) are obtained. The main tool for obtaining the results is the second order asymptotic linearity of the pertaining linear rank statistics which is proved here under the assumption that the score-generating function ? has some jump-discontinuities.     

Complainers and noncomplainers revisited: Another look at the data

The point of departure for the present article is previous attempts to profile complaining, dissatisfied consumers. By reviewing the previous literature, three “models” were identified: the “resource”, the “learning” and the “personality” model respectivey. An empirical test of the three models reveals only modest differences between complaining and noncomplaining consumers. Marketplace participation was found to be the most meaningful explanatory factor.     

Iterative analysis of two- and three-way designs

The iterative analysis of block designs is considered and an iterative method for analysing three-way designs is derived using a well known mathematical result. The results presented are discussed with the help of examples.     

Theory of factorial designs of the parallel flats type. I: the coefficient matrix

Let GF(s) be the finite field with s elements.(Thus, when s=3, the elements of GF(s) are 0, 1 and 2.)Let A(r×n), of rank r, and c_i(i=1,…,f), (r×1), be matrices over GF(s). (Thus, for n=4, r=2, f=2, we could have A=[¹¹¹⁰₀₁₂₁], c₁=[¹₀], c₂=[⁰₂].) Let T_i (i=1,…,f) be the flat in EG(n, s) consisting of the set of all the s^n?r solutions of the equations At=c_i, wheret′=(t₁,…,t_n) is a vector of variables.(Thus, EG(4, 3) consists of the 3⁴=81 points of the form (t₁,t₂,t₃,t₄), where t's take the values 0,1,2 (in GF(3)). The number of solutions of the equations At=c_i is s^n?r, where r=Rank(A), and the set of such solutions is said to form an (n?r)-flat, i.e. a flat of (n?r) dimensions. In our example, both T₁ and T₂ are 2-flats consisting of 3^4?2=9 points each. The flats T₁,T₂,…,T_f are said to be parallel since, clearly, no two of them can have a common point. In the example, the points of T₁ are (1000), (0011), (2022), (0102), (2110), (1121), (2201), (1212) and (0220). Also, T₂ consists of (0002), (2010), (1021), (2101), (1112), (0120), (1200), (0211) and (2222).) Let T be the fractional design for a sⁿ symmetric factorial experiment obtained by taking T₁,T₂,…,T_f together. (Thus, in the example, 3⁴=81 treatments of the 3⁴ factorial experiment correspond one-one with the points of EG(4,3), and T will be the design (i.e. a subset of the 81 treatments) consisting of the 18 points of T₁ and T₂ enumerated above.)In this paper, we lay the foundation of the general theory of such ‘parallel’ types of designs. We define certain functions of A called the alias component matrices, and use these to partition the coefficient matrix X (n×v), occuring in the corresponding linear model, into components X._j(j=0,1,…,g), such that the information matrix X is the direct sum of the X′._jX._j. Here, v is the total number of parameters, which consist of (possibly μ), and a (general) set of (geometric) factorial effects (each carrying (s?1) degrees of freedom as usual). For j≠0, we show that the spectrum of X′._jX._j does not change if we change (in a certain important way) the usual definition of the effects. Assuming that such change has been adopted, we consider the partition of the X._j into the X_ij (i=1,…,f). Furthermore, the X_ij are in turn partitioned into smaller matrices (which we shall here call the) X_ijh. We show that each X_ijh can be factored into a product of 3 matrices J, ζ (not depending on i,j, and h) and Q(j,h,i)where both the Kronecker and ordinary product are used. We introduce a ring R using the additive groups of the rational field and GF(s), and show that the Q(j,h,i) belong to a ring isomorphic to R. When s is a prime number, we show that R is the cyclotomic field. Finally, we show that the study of the X._j and X′._jX._j can be done in a much simpler manner, in terms of certain relatively small sized matrices over R.     

Testing optimality of experimental designs for a regression model with random variables

Tsukanov (Theor. Probab. Appl. 26 (1981) 173–177) considers the regression model $\text{E(}\text{y}\text{|}\text{Z}\text{)=}\text{Fp}\text{+}\text{Zq}$, $\text{D(}\text{y}\text{|}\text{Z}\text{)=σ}{}^2\text{I}{}_{\mathrm{n}}$, where $\text{y}\text{(n×1)}$ is a vector of measured values,$\text{F}\text{(n×k)}$ contains the control variables, $\text{Z}\text{(n×l)}$ contains the observed values, and $\text{p}\text{(k×1)}$ and $\text{q}\text{(l×1)}$ are being estimated. Assuming that $\text{Z}\text{=}\text{FL}\text{+}\text{R}$, where $\text{L}\text{(k×l)}$ is non-random, and the rows of $\text{R}\text{(n×l)}$ are i.i.d. $\text{N(}\text{0}\text{,Σ)}$, we extend Tsukanov's results by (i) computing E(detH_p), where H_p is the covariance matrix of p?, the l.s.e. of p, (ii) considering ‘optimality in the mean’ for the largest root criterion, (iii) discussing these equations when the matrix R has a left-spherical distribution.     

Developing and transferring behavioral technologies for children and youth

Behavioral researchers have developed a variety of technologies for improving the capacities of children and their caregivers. Despite the availability of behavioral technologies for children and youth, their widespread adoption and sustained use has been limited. Characteristics for appropriate (e.g., sustainable, effective) technologies for children and youth are suggested here, and strategies for research and development of these methods are described. This paper outlines the process of transferring behaviorial technologies including the phases of awareness, interest, assessment, trial, implementation, maintenance, and reinvention. Finally, issues implicit in the process of transferring behavioral technologies for children and youth are discussed.     

三层B／S结构网上选课系统设计与实现

论述了基于三层B/S结构的网上选课系统的设计与实现方法。系统利用三层结构的优点实现了网上的学生选课、选课管理、选课查询等功能。